B. Answer each question. Show all work where applicable. 1. Use the Division Algorithm to find the quotient (q), and remainder (r) when 100 is divided by 12. 2. Use the Euclidean Algorithm to find the greatest common divisor of 412 and 31. 3. Find the complete solution to the following equation: 2x + 3y = 1. C. Prove each of the following theorems. 1. Theorem: If a, b, and c are integers such that alb and blc, then alc. 2. Theorem: If a, b, c, and d are integers and alb and cld, the ac|bd.